Question

Which of the following terms related to the Root Loci technique originates from the centre of gravity of the centroid and goes to infinity at some definite angle?
1. Angle of arrival or departure
2. Asymptotes of Root Loci
3. Symmetry of root
4. Symmetry of Root Locus

Answer 1

Correct Answer - Option 2 : Asymptotes of Root Loci

Asymptotes of Root Loci:

Asymptote originates from the center of gravity or centroid and goes to infinity at definite some angle. Asymptotes provide direction to the root locus when they depart break away points.

Centroid:

It is the intersection of the asymptotes and always lies on the real axis. It is denoted by σ.

\(\sigma = \frac{{\sum {P_i} - \sum {Z_i}}}{{\left| {P - Z} \right|}}\)

ΣPi is the sum of real parts of finite poles of G(s)H(s)

ΣZi is the sum of real parts of finite zeros of G(s)H(s)